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\author{五六七}
\title{常微分方程第9周作业（8.3.1）}
%\date{2025年11月4日}

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\begin{document}

\maketitle

%\abstract{第8章第3节：例1、例子2、习题2(1)。}

\section{课后作业}
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\begin{enumerate}
\item  %例子8.3\#1
例子8.3.1. 
问题：作出平面动力系统在原点附近的相图：
\begin{eqnarray*}
\left\{ \begin{array}{rcl}
\frac{dx}{dt} &=& 2x+3y, \\
\frac{dy}{dt} &=& 2x-3y.\\
\end{array}\right.
\end{eqnarray*}

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\item  %例子8.3\#2
例子8.3.2. 
作出平面动力系统在原点附近的相图：
\begin{eqnarray*}
\left\{ \begin{array}{rcl}
\frac{dx}{dt} &=& 3x, \\
\frac{dy}{dt} &=& 2x+y.\\
\end{array}\right.
\end{eqnarray*}

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\item  %习题8.3\#2(1)
习题8.3.2(1). 
判断下列方程的奇点 $(0,0)$ 的类型，并作出该奇点附近的相图：
$$
dx/dt = 4y-x, \,\, dy/dt = -9x+y. 
$$

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\end{enumerate}

\end{document}
